The human brain can be described as containing a number of functional regions. For a given task, these regions, as well as the connections between them, play a key role in information processing in the brain. However, most existing multi-voxel pattern analysis approaches either treat multiple functional regions as one large uniform region or several independent regions, ignoring the connections between regions. In this paper, we propose to model such connections in an Hidden Conditional Random Field (HCRF) framework, where the classifier of one region of interest (ROI) makes predictions based on not only its voxels but also the classifier predictions from ROIs that it connects to. Furthermore, we propose a structural learning method in the HCRF framework to automatically uncover the connections between ROIs. Experiments on fMRI data acquired while human subjects viewing images of natural scenes show that our model can improve the top-level (the classifier combining information from all ROIs) and ROI-level prediction accuracy, as well as uncover some meaningful connections between ROIs.

In this study, we present a method for estimating the mutual information for a localized pattern of fMRI data. We show that taking a multivariate information approach to voxel selection leads to a decoding accuracy that surpasses an univariate inforamtion approach and other standard voxel selection methods. Furthermore,we extend the multivariate mutual information theory to measure the functional connectivity between distributed brain regions. By jointly estimating the information shared by two sets of voxels we can reliably map out the connectivities in the human brain during experiment conditions. We validated our approach on a 6-way scene categorization fMRI experiment. The multivariate information analysis is able to find strong information flow between PPA and RSC, which confirms existing neuroscience studies on scenes. Furthermore, by exploring over the whole brain, our method identifies other interesting ROIs that share information with the PPA, RSC scene network,suggesting interesting future work for neuroscientists.

Regularized Least Squares (RLS) algorithms have the ability to avoid over-fitting problems and to express solutions as kernel expansions. However, we observe that the current RLS algorithms cannot provide a satisfactory interpretation even on a constant function. On the other hand, while kernel-based algorithms have been developed in such a tendency that almost all learning algorithms are kernelized or being kernelized, a basic fact is often ignored: The learned function from the data and the kernel fits the data well, but may not be consistent with the kernel. Based on these considerations and on the intuition that a good kernel-based inductive function should be consistent with both the data and the kernel, a novel learning scheme is proposed. The advantages of this scheme lie in its corresponding Representer Theorem, its strong interpretation ability about what kind of functions should not be penalized, and its promising accuracy improvements shown in a number of experiments. Furthermore, we provide a detailed technical description about heat kernels, which serves as an example for the readers to apply similar techniques for other kernels. Our work provides a preliminary step in a new direction to explore the varying consistency between inductive functions and kernels under various distributions.

In the Gaussian process regression the observation model is commonly assumed to be Gaussian, which is convenient in computational perspective. However, the drawback is that the predictive accuracy of the model can be significantly compromised if the observations are contaminated by outliers. A robust observation model, such as the Student-t distribution, reduces the influence of outlying observations and improves the predictions. The problem, however, is the analytically intractable inference. In this work, we discuss the properties of a Gaussian process regression model with the Student-t likelihood and utilize the Laplace approximation for approximate inference. We compare our approach to a variational approximation and a Markov chain Monte Carlo scheme, which utilize the commonly used scale mixture representation of the Student-t distribution.

Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum, etc., in finding its optimum. In this paper, we propose the Heavy-tailed Symmetric Stochastic Neighbor Embedding (HSSNE) method, which is a generalization of the t-SNE to accommodate various heavy-tailed embedding similarity functions. With this generalization, we are presented with two difficulties. The first is how to select the best embedding similarity among all heavy-tailed functions and the second is how to optimize the objective function once the heave-tailed function has been selected. Our contributions then are: (1) we point out that various heavy-tailed embedding similarities can be characterized by their negative score functions. Based on this finding, we present a parameterized subset of similarity functions for choosing the best tail-heaviness for HSSNE; (2) we present a fixed-point optimization algorithm that can be applied to all heavy-tailed functions and does not require the user to set any parameters; and (3) we present two empirical studies, one for unsupervised visualization showing that our optimization algorithm runs as fast and as good as the best known t-SNE implementation and the other for semi-supervised visualization showing quantitative superiority using the homogeneity measure as well as qualitative advantage in cluster separation over t-SNE.

The method of common spatio-spectral patterns (CSSPs) is an extension of common spatial patterns (CSPs) by utilizing the technique of delay embedding to alleviate the adverse effects of noises and artifacts on the electroencephalogram (EEG) classification. Although the CSSPs method has shown to be more powerful than the CSPs method in the EEG classification, this method is only suitable for two-class EEG classification problems. In this paper, we generalize the two-class CSSPs method to multi-class cases. To this end, we first develop a novel theory of multi-class Bayes error estimation and then present the multi-class CSSPs (MCSSPs) method based on this Bayes error theoretical framework. By minimizing the estimated closed-form Bayes error, we obtain the optimal spatio-spectral filters of MCSSPs. To demonstrate the effectiveness of the proposed method, we conduct extensive experiments on the data set of BCI competition 2005. The experimental results show that our method significantly outperforms the previous multi-class CSPs (MCSPs) methods in the EEG classification.

Recent work has led to the ability to perform space efficient, approximate counting over large vocabularies in a streaming context. Motivated by the existence of data structures of this type, we explore the computation of associativity scores, other- wise known as pointwise mutual information (PMI), in a streaming context. We give theoretical bounds showing the impracticality of perfect online PMI compu- tation, and detail an algorithm with high expected accuracy. Experiments on news articles show our approach gives high accuracy on real world data.

Aiming towards the development of a general clustering theory, we discuss abstract axiomatization for clustering. In this respect, we follow up on the work of Kelinberg, (Kleinberg) that showed an impossibility result for such axiomatization. We argue that an impossibility result is not an inherent feature of clustering, but rather, to a large extent, it is an artifact of the specific formalism used in Kleinberg. As opposed to previous work focusing on clustering functions, we propose to address clustering quality measures as the primitive object to be axiomatized. We show that principles like those formulated in Kleinberg's axioms can be readily expressed in the latter framework without leading to inconsistency. A clustering-quality measure is a function that, given a data set and its partition into clusters, returns a non-negative real number representing how `strong' or `conclusive' the clustering is. We analyze what clustering-quality measures should look like and introduce a set of requirements (`axioms') that express these requirement and extend the translation of Kleinberg's axioms to our framework. We propose several natural clustering quality measures, all satisfying the proposed axioms. In addition, we show that the proposed clustering quality can be computed in polynomial time.

We present a new empirical risk minimization framework for approximating functions from training samples for low-dimensional regression applications where a lattice (look-up table) is stored and interpolated at run-time for an efficient hardware implementation. Rather than evaluating a fitted function at the lattice nodes without regard to the fact that samples will be interpolated, the proposed lattice regression approach estimates the lattice to minimize the interpolation error on the given training samples. Experiments show that lattice regression can reduce mean test error compared to Gaussian process regression for digital color management of printers, an application for which linearly interpolating a look-up table (LUT) is standard. Simulations confirm that lattice regression performs consistently better than the naive approach to learning the lattice, particularly when the density of training samples is low.

Using machine learning algorithms to decode intended behavior from neural activity serves a dual purpose. First, these tools can be used to allow patients to interact with their environment through a Brain-Machine Interface (BMI). Second, analysis of the characteristics of such methods can reveal the significance of various features of neural activity, stimuli and responses to the encoding-decoding task. In this study we adapted, implemented and tested a machine learning method, called Kernel Auto-Regressive Moving Average (KARMA), for the task of inferring movements from neural activity in primary motor cortex. Our version of this algorithm is used in an on-line learning setting and is updated when feedback from the last inferred sequence become available. We first used it to track real hand movements executed by a monkey in a standard 3D motor control task. We then applied it in a closed-loop BMI setting to infer intended movement, while arms were restrained, allowing a monkey to perform the task using the BMI alone. KARMA is a recurrent method that learns a nonlinear model of output dynamics. It uses similarity functions (termed kernels) to compare between inputs. These kernels can be structured to incorporate domain knowledge into the method. We compare KARMA to various state-of-the-art methods by evaluating tracking performance and present results from the KARMA based BMI experiments.